相关论文: Deep Online Convex Optimization with Gated Games

This paper investigates distributed online convex optimization in the presence of an aggregative variable without any global/central coordinators over a multi-agent network, where each individual agent is only able to access partial…

Large learning rates, when applied to gradient descent for nonconvex optimization, yield various implicit biases including the edge of stability (Cohen et al., 2021), balancing (Wang et al., 2022), and catapult (Lewkowycz et al., 2020).…

Directly parameterizing and learning gradients of functions has widespread significance, with specific applications in inverse problems, generative modeling, and optimal transport. This paper introduces gradient networks (GradNets): novel…

Regret minimization is a powerful tool for solving large-scale extensive-form games. State-of-the-art methods rely on minimizing regret locally at each decision point. In this work we derive a new framework for regret minimization on…

This paper studies bandit convex optimization with constraints, where the learner aims to generate a sequence of decisions under partial information of loss functions such that the cumulative loss is reduced as well as the cumulative…

Gating is a key feature in modern neural networks including LSTMs, GRUs and sparsely-gated deep neural networks. The backbone of such gated networks is a mixture-of-experts layer, where several experts make regression decisions and gating…

In this paper, we analyze the problem of online convex optimization in different settings, including different feedback types (full-information/semi-bandit/bandit/etc) in either stochastic or non-stochastic setting and different notions of…

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…

A candidate explanation of the good empirical performance of deep neural networks is the implicit regularization effect of first order optimization methods. Inspired by this, we prove a convergence theorem for nonconvex composite…

In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming…

Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…

To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms…

In this book, I introduce the basic concepts of Online Learning through the modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order…

A constrained version of the online convex optimization (OCO) problem is considered. With slotted time, for each slot, first an action is chosen. Subsequently the loss function and the constraint violation penalty evaluated at the chosen…

Most of the literature on learning in games has focused on the restrictive setting where the underlying repeated game does not change over time. Much less is known about the convergence of no-regret learning algorithms in dynamic multiagent…

Universal online learning aims to achieve optimal regret guarantees without requiring prior knowledge of the curvature of online functions. Existing methods have established minimax-optimal regret bounds for universal online learning, where…

Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which…

Computational models of vision have traditionally been developed in a bottom-up fashion, by hierarchically composing a series of straightforward operations - i.e. convolution and pooling - with the aim of emulating simple and complex cells…

We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an…

Gating mechanisms are widely used in neural network models, where they allow gradients to backpropagate more easily through depth or time. However, their saturation property introduces problems of its own. For example, in recurrent models…